Department of
Mathematics and Statistics, University of Strathclyde
• — Virtual Workshop, 15^{th}
& 16^{th} June 2021
The main
research interests of the group lie in aspects of enumerative, bijective,
algebraic and topological combinatorics, with applications to computer
science, physics and biology. Much of our work has focussed on patterns in
permutations and other combinatorial objects. Central to this area is concept
of a permutation class, which is a downset under the permutation containment
order. The study of these structures began in the 1960s with Donald Knuth’s
investigation of computational sorting devices, which is still an active area
of research. Subsequently, they have been used to analyse models of genome
rearrangement, the layout of integrated circuits, and gas models in
statistical physics, among other things. 

Sergey Kitaev
(Head of Group)
Sergey’s
research interests encompass aspects of enumerative and algebraic
combinatorics, combinatorics on words, and graph theory. Successes include
the enumeration of (2+2)free posets via an encoding of them as ascent
sequences. Sergey is the author of two monographs, one on patterns in
permutations and words, and the other on words and graphs. Recently, he has
pioneered the theory of wordrepresentable graphs (a topic on the boundary of
graph theory and combinatorics on words, with roots in algebra), including
giving an effective characterization in terms of graph orientations. 



David Bevan
David’s
research interests mainly concern enumerative and asymptotic questions,
particularly in relation to permutations. Achievements include an explicit
formula for the growth rate of grid classes of permutations, and a structural
characterisation of the class of permutations avoiding 1324 together with new
bounds on its growth rate. Current research topics include the evolution of
the random permutation (as the number of its inversions increases),
permutation limits at different scales, and enumerative and structural
questions concerning permutation grid classes. 



Einar
Steingrímsson
Einar’s
research interests primarily concern algebraic combinatorics, particularly in
relation to permutation patterns, and with an emphasis on permutation
statistics. He pioneered the concept of a vincular pattern, which has since
been generalised further by the notion of a mesh pattern. A particular focus
has been on the topology and Möbius function of intervals in the poset of
permutations ordered by pattern containment. Other recent work has concerned
the Abelian sandpile model, and the introduction and analysis of new
combinatorial structures whose motivation comes from particle physics. 
• Dan
Threlfall (from 2020)
• Noura
Alshammari (from 2021)
• 26th British
Combinatorial Conference, 3–7 July 2017
• Permutation Patterns 2012,
11–15 July 2012
• FPSAC 2011, 13–17
June 2011
• Anders Claesson (2011–2016; now Professor at the University of Iceland,
Reykjavík)
• Mark
Dukes (2011–2016; now Lecturer at University College,
Dublin)
• Thomas
Selig (2015–2018; now
Assistant Professor at Xi'an JiaotongLiverpool
University, Suzhou, China)
• Jason Smith (2015–2018; now
Lecturer at Nottingham Trent University)
• Kittitat Iamthong (2018–2021) Encoding graphs by
words and morphisms
• Marc Glen (2016–2019) On wordrepresentability of polyomino
triangulations and crown graphs
• Jason Smith (2012–2015) On the Möbius
function and topology of the permutation poset
• Stuart Hannah (2011–2015) Interval order
enumeration
• Connecting
physics models via permutations (Einar Steingrímsson, Leverhulme Research
Fellowship, 2018–2020)
• New
combinatorial perspectives on the Abelian sandpile model (Mark Dukes and
Einar Steingrímsson, EPSRC, 2015–2018)
• The
Möbius function of the poset of permutations (Einar Steingrímsson, EPSRC, 2015–2018)
• Finding structure in sets of
permutations (Anders Claesson, Icelandic Research Fund, 2014–2016)
• Combinatorics of permutations and
words (Einar Steingrímsson, Anders Claesson, Sergey Kitaev and Mark Dukes,
Icelandic Research Fund, 2009–2012)